Cone (EntityTopic, 11)
From Hi.gher. Space
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[!z] ⇒ circle of radius (''r''-''rnh''<sup>-1</sup>)</blockquote> | [!z] ⇒ circle of radius (''r''-''rnh''<sup>-1</sup>)</blockquote> | ||
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{{Rotope Nav|11|12|13|(II)I<br>Cylinder|(II)'<br>Cone|((II)I)<br>Torus|hedra}} | {{Rotope Nav|11|12|13|(II)I<br>Cylinder|(II)'<br>Cone|((II)I)<br>Torus|hedra}} | ||
Revision as of 20:04, 17 August 2007
Geometry
A cone is a special case of a pyramid where the base is a circle.
The cone is one of the few curved polyhedra that satisfy Euler's F + V = E + 2.
Equations
- Variables:
r ⇒ radius of base of cone
h ⇒ height of cone
- All points (x, y, z) that lie on the surface of a cone will satisfy the following equations:
Unknown
- All points (x, y, z) that lie on the edges of a cone will satisfy the following equations:
x2 + y2 = r2
z = 0
- The hypervolumes of a cone are given by:
total edge length = 2πr
surface area = πr2 + πrsqrt(h2 + r2)
volume = πr2h3-1
- The planar cross-sections (n) of a cone are:
[!x,!y] ⇒ Unknown
[!z] ⇒ circle of radius (r-rnh-1)
